Acosta tweeted a video of him surrendering his "hard pass", or press credentials to the Secret Service. "This conduct is absolutely unacceptable".
The "Jersey Girl Embarrassed by Bob Menendez", as Conway has dubbed herself on Twitter, also said that she doesn't think "anybody should have - any young woman, particularly - should have somebody swiping away at them, grabbing the microphone back".
Many outlets expressed concern at the fact that a White House staffer attempted to take the microphone away from Acosta, who wouldn't stop talking even though he received answers to two different questions.
Mr Acosta questioned Mr Trump's reference to the caravan as an invasion, and Mr Trump defended the term.
Acosta steadfastly refuted Sanders' accusation, which she made via Tweetstorm, calling it "a lie". He simply kept a firm grip on the mic when she tried to grab it and said, "Pardon me, ma'am", and continued trying to ask President Trump a second question about Special Counsel Robert Mueller's Russian Federation investigation. "You are are a rude, awful person".
Describing Acosta's behaviour as "disgusting and outrageous", the White House Press Secretary, Sarah Sanders, in a statement on Wednesday said, "As a result of today's incident, the White House is suspending the hard pass of the reporter involved until further notice".
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The decision to expel Acosta came just hours after confirmation that the Republican Party had lost control of the US House of Representatives on Wednesday. As the Joker put it in Christopher Nolan's The Dark Knight: "I don't wanna kill you". The White House has accused him of provoking confrontations, and he, in turn, has become a favorite target of insults lobbed by Trump's supporters, particularly during the president's raucous rallies. "History will not be kind to you", CNN Matt's Dornic, vice president of communications and digital partnerships, wrote on Twitter Thursday.
When the president tried to go to another journalist, Acosta declined to give up the microphone and asked about possible indictments by special counsel Robert Mueller based on the ongoing investigation into Trump's presidential campaign. "We stand by our statement".
Looking back at Acosta, Trump added: "The way you treat [press secretary] Sarah Huckabee is awful, and the way you treat other people is frightful".
Acosta tweeted that this was "a lie".
The White House sought to brush aside suggestions it is stifling a free press.
CNN have released a statement on the incident and have included their full support for the reporter.
Following one of many fiery exchanges with the Trump administration, Acosta railed against Trump in 2017 and called him "a purveyor of fake news".